SAN DIEGO, California (CNN) --A huge American flag unfurled on deck Wednesday and a cheering crowd greeted the 6,000 sailors of the USS Nimitz, which just completed an eight-month deployment for the war in Iraq.

An airplane swept by with a banner reading, "Welcome Home USS Nimitz Heroes" and more than 10,000 people waved flags and homemade signs to welcome the troops back at North Island Naval Air Station.

One hundred twenty-three new fathers were holding their children for the first time, including Seaman Timothy Clague, whose daughter Brianna was born just six days after the Nimitz left.

"I've been thinking about her all the time on the boat. Every day, every waking moment," Clague said, cradling Brianna. "Once I saw her, it was the best feeling in the world."

"I'll never forget it," his wife Heather Clague chimed in. "I've been fantasizing about it, falling asleep thinking about this moment, thinking it would never get here. I really don't know what to say right now. It was wonderful."

Seaman Robert Ayala was holding 4-month-old Nathaniel for the first time. "It's a dream come true, honestly. Every second it's been thinking about him, my wife, coming home. All three at once, you can't beat that."

His wife Stephanie was nearly speechless.

"I'm at a total loss," she said. "I'm going to be a basket case the rest of the day."

The hardest part, she said, was during intense fighting when her husband was not available to talk.

"There was a good period of time when I didn't hear anything from him. But the e-mails and the calls in port made everything easier," she said. "I think it was easier than I thought it would be."

After the ship docked, shortly after 9 a.m. (noon EST), the first people off were two sailors who had won an onboard raffle to be the "first kissers."

Rena Murphy spent $100 on raffle tickets to win a kiss with her boyfriend, Seaman Nelson Buckley. Because Murphy was away in training when the Nimitz left port, they hadn't seen each other for 13 months.

"It was absolutely fantastic," Buckley said, after the two disentangled.

"The waiting is killer," said Murphy, tears running down her cheeks. "You're lucky if the e-mails work. You've got to try over and over again.

"To be able to talk to him face to face and have a real conversation is absolutely wonderful."

The other sailor to win the raffle was Barry Parnell. His wife Lucy called her raffle tickets "the best $10 I ever spent."

"It was everything I expected," she said after the kiss.

Her husband: "It was more."

"Deployments are always tough," Capt. Robert Gilman told CNN shortly before docking. "You think, 'Can I do this?' But the crew rose to the occasion, and they met the challenge and they did it well."

Gilman was looking forward to a reunion with his wife of 26 years, Eliza.

"I'm very proud of my husband and very proud of the crew," she said as she waited.

The Nimitz carrier is part of an eight-ship battle group that flew more than 6,500 missions during the Iraq war.